Concentrated cohesive sediment suspensions exhibit strongly non-Newtonian and time-dependent behaviour caused by particle interactions, which complicates the prediction of their strain or shear rate response to applied forces. In this paper the rheological properties of both China clay, an artificial mud, and Caland channel mud, a natural mud, are investigated. Four types of experiments are involved: equilibrium flow curves, stepwise changes in shear rate to investigate the time-scale of structural changes, experiments in which the increase in yield stress with recovery time after structural destruction was measured, and harmonic oscillation experiments to investigate the visco-elastic behaviour of mud at low strains. For these measurements both shear rate and shear stress controlled instruments were used. Equilibrium flow curves revealed strong shearthinning behaviour for China clay, which was much less observed for Caland channel mud. Experimental results are described in terms of a thixotropic model including two structural parameters to account for structural changes within the material, one to describe short-term changes when the material is flowing, another to describe long-term changes when the material is at rest. From experiments with stepwise changes in shear rate it followed that the time-scale of structural changes is in the order of seconds. Both materials showed a yield stress, Caland channel mud being the more cohesive mud. Yield stress measurements as a function of rest time after pre-shearing showed that the time-scale for the build-up of an interconnected aggregate structure is in the order of 104-105 s. From harmonic oscillation experiments it can be concluded that the range within which muds exhibit linear visco-elastic behaviour is limited to strains smaller than approximately 1%.